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Hogsheads and butts: Lessons from an 1840s textbook

In the recent move to the new Hildreth Elementary School building, the oldest item found in the unpacking was a textbook with the date 1849 and a name written on the first page of the small, coverless book. There were several other schoolbooks from the 1800s in the same box, and one wonders how many moves they had been through in their long lives. The texts must have originally been used in one of the nine district schools throughout Harvard and then perhaps moved to another when some were consolidated. They would have found their way to the central elementary school, built on Mass. Ave. in 1905, when the district system was finally abolished.

From 1905 on, how many different teachers continued to keep that carton of old books, moving it with them when parts of the school building were added or demolished? And why? Perhaps they suspected that someone in a future century would find them of historical interest, and the old school books do, in fact, give us information from which to piece together a picture of some aspects of education and of everyday life during the mid- to late-1800s.

The oldest book of the lot, an arithmetic text published in Boston in 1847, was written by Benjamin Greenleaf, and the title page notes, “Designed for Common Schools.” This is a reference to the educational reform movement of the 1830s, which began in Massachusetts and became widespread in New England. Championed by Horace Mann, the movement was an institutional response to the rapid urban industrialization that brought fear of social fragmentation and moral and cultural decay. The common school movement advocated free education for all white children and state control over public schools. It also argued for the establishment of “normal schools” that would set norms for teacher training. Greenleaf’s preface has a notice acknowledging this need and advertising more immediate help for teachers: “A KEY to this work, in which the method of solving the questions is fully exhibited, has just been published, for the convenience of teachers only.”

The need for teacher training is reflected in an 1868 report from one of Harvard’s district supervisors: “It is by no means an uncommon thing for the committee to have the mortification of seeing teachers call out classes and hear recitations in what they themselves don’t understand and don’t try to.” Improvement is evidenced in another district evaluation of 1884: “Eliza Fuzzard is a member of the Bridgewater Normal School, and our experience with her is evidence of the success of the normal school training.”

A national arithmetic

Greenleaf’s title is lengthly: “Introduction to the National Arithmetic, on the Inductive System Combining the Analytic and Synthetic Methods with the Canceling System; in which the Principles of Arithmetic are Explained and Illustrated in a Familiar Manner,” and it seems to be in itself an advertisement for the common school. Calling it “National Arithmetic” is an appeal to the movement’s belief in giving all children an opportunity for the same kind of education. This idea is furthered by the assurance that the explanations and illustrations will be “familiar,” which seems here to mean “common to all.” In saying the author “commends this small volume to the candor of an enlightened Public,” Greenleaf appeals to those supporting this new, more democratic education.

A common perception is that education until well into the 20th century was largely rote learning through recitation and drills. There’s much in Greenleaf’s book to support this. The student was expected to know the Numeration Table, “to be familiar with the names from Units to Tridecillions [sic] and from Tridecillions to Units so that he may repeat them with facility either way.” For vulgar fractions (vulgar here meaning “ordinary, of the common people,” further evidence that the text is for use in the common school system), the pupil must “commit all the definitions before he commences mental operations.”

More than rote

But Greenleaf’s title suggests that rote memorization must be complemented by inductive reasoning, through which the student will discover patterns and principles based on many examples, and by the analytic method, which breaks down math functions into parts so that students understand how math works. Greenleaf begins the sections on math functions by describing in great detail how any figure in the first place, from right to left, denotes its simple value; but in the second place, denotes ten times its simple value, and so on. There are friendly explanations of all functions. For example, in the given problem “From 624 Take 342,” the process is described: “In attempting to take the 4 tens, we find a difficulty, as 4 cannot be taken from 2. We therefore borrow 1 (hundred) from the 6 (hundred), which being equal to 10 tens, we add it to the upper line, making 12 tens, and 8 (tens) remain, which we set down. We then proceed …” (Even this severely math-challenged writer might have understood what she was doing given this explanation rather than just being told to “borrow the one.”)

The controversy between rote learning and inductive reasoning is reflected in a 1868 Harvard district school report, where a teacher evaluation applauded the fact that the “lessons were well and promptly recited, showing a familiarity with the textbooks.” Where scholars did not progress, it was suggested that “more thorough drill” would remedy the problem. But, on the other hand, Miss Graves of District No.1 was criticized for “telling [her students] what they ought to have found out for themselves.”

It was surprising to find that the great majority of the exercises in the text are word problems. Not only do they make the exercises more interesting and relevant, they give students practice in reading at the same time. They also reveal a lot about the values and livelihoods of people at that time.

Practical math

Many of the problems relate to farming—buying and selling cows and yokes of oxen, the acreage of farms, transactions in loads of hay, the price of a horse and chaise—and, as in the following problem, more than one might want to know about the parts of an ox: “The hind quarters of an ox weighed 375 pounds each; the fore quarters 315 each; the hide weighed 96 pounds, and the tallow 87 pounds. What was the whole weight of the ox?”

The new industrialization and merchant capitalism are reflected in problems such as, “A factory cost 68,255 dollars. Supposing the sum divided into 365 shares, what is the expense of each?” and “If a mechanic deposit annually in the Savings Bank 407 dollars, what will be the sum deposited in 27 years?”

Numerous tables and problems involving weights and measures show how many have fallen out of use. We no longer need to know the number of gallons in a hogshead and hogsheads in a butt, or definitions of a pennyweight, scruple, and nail (of cloth). Exercises about the cost of household items show a vastly different economy: “1 pound of raisins cost 6 cents . . . a good pair of boots is worth 5 dollars . . . and 6 dollars buy a barrel of flour.”

Not surprisingly, the subjects of all but a handful of problems use male names—James, John, Henry, Peter, and an occasional Enoch—or professions—a farmer, carpenter, tailor, merchant. Only once in a while does Jane or Lydia divide 20 apples among friends or a mother give her daughter $10 to go shopping. An interesting example of this gender bias is in the following problem: “A man gave half of his estate to his wife, one third of what remained to his son, and the residue was equally divided among his 7 daughters, who received each 124 dollars; what was the whole estate?”

Ardent spirits

Another problem shows the ever-present interest in ardent spirits and the astonishing consumption of it. “There were distilled in the United States in 1840 thirty-six millions three hundred forty-three thousand two hundred thirty-six gallons of ardent spirits; and the number of free white males, over 15 years, is four million seventy-four thousand nine hundred fifteen; now supposing the liquor to be drank by one third of those persons in one year, what quantity would each consume?” The temperance movement was underway by the time this book was written. Is this problem just being factual about the alcohol use it describes? Or is the answer—more than 26 gallons—meant to be a condemnation?

This 174-year-old arithmetic book and the other old texts, shepherded from one Harvard grade school to another over time, are now ensconced at the Historical Society, where they will continue to tell their stories of earlier times.

Next time: Spelling, science, and recess

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